The term borehole generally designates the result of a drilling operation in the earth, either vertically, horizontally and/or deviated using a drill string, comprising a drill bit at its lower end. At its upper end or top end, the drill string is driven by a drive system at the earth surface, called a top drive or rotary table. The top drive or rotary table is driven by an electric motor, or any other type of drive motor, providing a rotational movement to the drill bit in the borehole.
Typically, the drill string is a structure of a plurality of tubulars or pipes, threadedly connected to each other. A typical drill string may have a length of several hundreds or thousands of meters.
The lower part of the drill string is called the bottom hole assembly, BHA, at which the cutting tool for drilling the borehole, also called the drill bit, connects.
The drill string is hollow, such that drilling fluid can be pumped down towards the bottom hole assembly and through nozzles in the bit, for lubrication purposes. The drilling fluid is circulated back up the annulus, i.e. the space between the outer circumference of the drill string and the borehole wall, to transport cuttings from the drill bit to the earth surface.
A borehole may be drilled for many different purposes, including the extraction of water or other liquid (such as oil) or gases (such as natural gas), as part of a geotechnical investigation, environmental site assessment, mineral exploration, temperature measurement or as a pilot hole for installing piers or underground utilities, for example.
The bottom hole assembly is rigid in torsional direction as it is relatively short and thick-walled. In use, the bottom hole assembly experiences lateral deflections due to compressive force. The drill string is a slender and flexible structure due to its long length and relative small wall thickness. During drilling, numerous vibrations in the borehole equipment and, in particular, in the drill string, are generated. In a rotary drill string and bottom hole assembly, torsional, axial and longitudinal or lateral vibrations may occur.
In general, axial vibrations may cause bit bounce, which may damage bit cutters and bearings. Lateral vibrations may be very destructive and may create large shocks as the bottom hole assembly impacts the wall of the borehole. Lateral vibrations may drive the system into backward whirl, creating high-frequency large-magnitude bending moment fluctuations, resulting in high rates of component and connection fatigue. Imbalance in an assembly may cause centrifugally induced bowing of the drill string, which may produce forward whirl and results in one-sided wear of components. Torsional vibrations result, among others, in stick-slip motions or oscillations of the drill string alongside the borehole.
Stick-slip is a phenomenon caused by frictional forces between surfaces of the drill bit and/or the drill string contacting the earth formation surface or the inner wall surface of the borehole. The surfaces of the drill bit and/or the drill string on the one hand and the surfaces of the earth formation and borehole on the other hand, alternatingly may stick to each other or slide over each other, with a corresponding change in the force of friction.
In practice, this friction force shows a non-linear behaviour and, in extreme cases, the friction may become so large that the drill bit, i.e. the bottom hole assembly, temporarily comes to a complete standstill, called the stick mode. During the stick mode, the continuing rotational drive speed or motion of the drive system winds-up the drill string. If the torque build-up in the drill string is large enough to overcome the static friction, the bottom hole assembly starts rotating again, called the slip mode. This, however, may cause a sudden jump or a stepwise increase in the angular acceleration of the movement of the drill bit, inter alia in that the dynamic friction encountered by the drill string and bottom hole assembly is less than the static friction, and may result in excessive wear thereof. Stick and slip modes may follow each other rather quickly in a regular, periodic manner.
When stick-slip occurs, the effectiveness of the drilling process is affected, such that a planned drilling operation may be delayed over as much as a few days, with the risk of penalty fees and the like.
Among others for mitigating the impact of torsional vibrations and resonance in the drill string and the occurrence and impact of stick-slip operation and oscillations, the rotational drive speed of the drive system of the borehole equipment is controlled by a speed controller, the parameters of which are set and tuned to the relevant operational parameters of the borehole equipment. The term “mitigating” has to be construed to include controlling, alleviating, reducing, soften, tempering, relieving, and like meanings, up to and including avoiding torsional vibrations and stick-slip oscillations.
The operational parameters of the borehole equipment, among others, depend on the mechanical properties of the top end drive or surface drive and the string geometry. In practice, the spring geometry parameters need to be provided by the driller by entering, via a keypad of an input/output interface of the speed controller, for example, the inner and outer diameters and length of the drill string tubulars or pipes, and the drill collars of the bottom hole assembly at which the drill bit rests from a spread-sheet or the like. It will be appreciated that, instead of entering the mechanical properties of the borehole equipment itself, one may enter the values of the parameters of the speed controller from a spread-sheet or table or the like, already calculated based on a particular drill string geometry used.
As drilling progresses, the string geometry, i.e. the length and mechanical properties of the tubulars changes due to the lengthening of the drill string and/or changes in the bottom hole assembly. As will be appreciated, each time when extending the drill string, for example by a stand comprising two or three single joints of drill pipe, the dynamics of the borehole equipment change. In practice, this necessitates to retune the parameters of the speed controller approximately every 100 to 200 m of drilling, for example.
Each time determining and manually inputting into the speed controller the operational parameters of the borehole equipment or equivalent values while drilling progresses, is cumbersome to the driller and may introduce errors that may result in reduced Rate Of Penetration, ROP, of the borehole equipment, generally expressed in meters per hour, m/h.
As mentioned above, torsional vibrations and resonance in the drill string of borehole equipment are friction related. Accordingly, external aspects such as the type of earth formation, the type of borehole to be drilled, i.e. vertically, horizontally or askew, the type of mud used, etc., besides the internal mechanical properties of the borehole equipment, all have an influence on the actual operation of the borehole equipment and the occurrence and intensity of the torsional vibrations, drill string resonance frequency and stick-slip operation that may occur during drilling.
In practice, among others for optimally controlling a drilling operation by borehole equipment, both from a technical and an economical point of view, there is a need for automatically modelling borehole equipment by a representative computational model, in particular while drilling a borehole in an earth formation.